MATH 111 Midterm: MATH 111 Amherst F14M111 2803 29Oloo

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turquoisegnu128

15 Feb 2019

School

Amherst College

Department

Mathematics and Statistics

Course

MATH 111

Professor

All

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Document Summary

Do all work in the blue books provided. Mark your answers clearly, and write down all steps used to obtain your answers: [18 points] compute the following derivatives. Do not simplify your answers. (a) (b) (c) Please justify your reasoning. (a) lim x 1 x2 5x + 4 x2 4x + 3 x3 4x + 4. 1 x g(x2) + 1 (b) lim x (c) lim x 1. 1: [15 points] sand is added to a pile on the ground. Suppose that at time t, the pile has. Give reasons. (f) for which numbers x is f (x) < 0: [20 points] we have a right triangle whose sides are changing with respect to time. When solving this problems, be sure to follow the guidelines used in class: [20 points] do a curve graphing for y = 3x4+4x3. Please indicate where the function is increasing and decreasing and where the graph is concave up and concave down.

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3
(iv)
(v)
(vi)

3 (iii)

Problem 4 Circle your answer. a) (6 points) If f(x) = 2x + 3x2 - 361 + 5, then the tangent line to the graph y= f(x) is horizontal when i) 1 = -2,3 ii) I = 2,-3 iii) r = 0 iv) not listed b) [6 points] Suppose Given h(x) = f(g(T)), where g(2) = 3, g'(2) = 7, f'(2) = -1 and 1'(3) = -2. Then h'(2) is equal to i) - 1 ii) -2 iii) - 14 iv) not listed (x+3)(1 - 1)3 c) (6 points) The function f(1) == (x2 - 2x + 1)(x + 3) wa has vertical asymptotes at i) x = -3,0 ii) = -3,0,1 iii) x = 0,1 iv) not listed d) (6 points] The solution to the initial value problem v'(x) = 473 – cos(x) +e", y(0) = 3 is i) y(x) = x + sin(x) + e* + 2 ii) y(I) = x4 – sin(x) +et+2 iii) y(x) = 2* – sin(1) + et + 3 iv) not listed

MATH 111 Midterm: MATH 111 Amherst F14M111 2803 29Oloo

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